5×3-32×2-36x-95x+3

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.

5x | + | 3 | 5×3 | – | 32×2 | – | 36x | – | 9 |

Divide the highest order term in the dividend 5×3 by the highest order term in divisor 5x.

x2 | |||||||||||

5x | + | 3 | 5×3 | – | 32×2 | – | 36x | – | 9 |

Multiply the new quotient term by the divisor.

x2 | |||||||||||

5x | + | 3 | 5×3 | – | 32×2 | – | 36x | – | 9 | ||

+ | 5×3 | + | 3×2 |

The expression needs to be subtracted from the dividend, so change all the signs in 5×3+3×2

x2 | |||||||||||

5x | + | 3 | 5×3 | – | 32×2 | – | 36x | – | 9 | ||

– | 5×3 | – | 3×2 |

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

x2 | |||||||||||

5x | + | 3 | 5×3 | – | 32×2 | – | 36x | – | 9 | ||

– | 5×3 | – | 3×2 | ||||||||

– | 35×2 |

Pull the next terms from the original dividend down into the current dividend.

x2 | |||||||||||

5x | + | 3 | 5×3 | – | 32×2 | – | 36x | – | 9 | ||

– | 5×3 | – | 3×2 | ||||||||

– | 35×2 | – | 36x |

Divide the highest order term in the dividend -35×2 by the highest order term in divisor 5x.

x2 | – | 7x | |||||||||

5x | + | 3 | 5×3 | – | 32×2 | – | 36x | – | 9 | ||

– | 5×3 | – | 3×2 | ||||||||

– | 35×2 | – | 36x |

Multiply the new quotient term by the divisor.

x2 | – | 7x | |||||||||

5x | + | 3 | 5×3 | – | 32×2 | – | 36x | – | 9 | ||

– | 5×3 | – | 3×2 | ||||||||

– | 35×2 | – | 36x | ||||||||

– | 35×2 | – | 21x |

The expression needs to be subtracted from the dividend, so change all the signs in -35×2-21x

x2 | – | 7x | |||||||||

5x | + | 3 | 5×3 | – | 32×2 | – | 36x | – | 9 | ||

– | 5×3 | – | 3×2 | ||||||||

– | 35×2 | – | 36x | ||||||||

+ | 35×2 | + | 21x |

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

x2 | – | 7x | |||||||||

5x | + | 3 | 5×3 | – | 32×2 | – | 36x | – | 9 | ||

– | 5×3 | – | 3×2 | ||||||||

– | 35×2 | – | 36x | ||||||||

+ | 35×2 | + | 21x | ||||||||

– | 15x |

Pull the next terms from the original dividend down into the current dividend.

x2 | – | 7x | |||||||||

5x | + | 3 | 5×3 | – | 32×2 | – | 36x | – | 9 | ||

– | 5×3 | – | 3×2 | ||||||||

– | 35×2 | – | 36x | ||||||||

+ | 35×2 | + | 21x | ||||||||

– | 15x | – | 9 |

Divide the highest order term in the dividend -15x by the highest order term in divisor 5x.

x2 | – | 7x | – | 3 | |||||||

5x | + | 3 | 5×3 | – | 32×2 | – | 36x | – | 9 | ||

– | 5×3 | – | 3×2 | ||||||||

– | 35×2 | – | 36x | ||||||||

+ | 35×2 | + | 21x | ||||||||

– | 15x | – | 9 |

Multiply the new quotient term by the divisor.

x2 | – | 7x | – | 3 | |||||||

5x | + | 3 | 5×3 | – | 32×2 | – | 36x | – | 9 | ||

– | 5×3 | – | 3×2 | ||||||||

– | 35×2 | – | 36x | ||||||||

+ | 35×2 | + | 21x | ||||||||

– | 15x | – | 9 | ||||||||

– | 15x | – | 9 |

The expression needs to be subtracted from the dividend, so change all the signs in -15x-9

x2 | – | 7x | – | 3 | |||||||

5x | + | 3 | 5×3 | – | 32×2 | – | 36x | – | 9 | ||

– | 5×3 | – | 3×2 | ||||||||

– | 35×2 | – | 36x | ||||||||

+ | 35×2 | + | 21x | ||||||||

– | 15x | – | 9 | ||||||||

+ | 15x | + | 9 |

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

x2 | – | 7x | – | 3 | |||||||

5x | + | 3 | 5×3 | – | 32×2 | – | 36x | – | 9 | ||

– | 5×3 | – | 3×2 | ||||||||

– | 35×2 | – | 36x | ||||||||

+ | 35×2 | + | 21x | ||||||||

– | 15x | – | 9 | ||||||||

+ | 15x | + | 9 | ||||||||

0 |

Since the remander is 0, the final answer is the quotient.

x2-7x-3

Divide (5x^3-32x^2-36x-9)/(5x+3)